8 problems

McMullen–Shephard's conjecture. For every $n\geq 3$, one has

Let $d=2k$ be a fixed even dimension, and let $\mathcal{B}_{2k}(X)$ denote the centrally symmetric polytope constructed from a set $X$ of $n$ equally spaced points on…

Let $P\subset\mathbb{R}^d$ be a centrally symmetric polytope, meaning that $x\in P$ implies $-x\in P$. It is 2-neighborly if every pair of non-antipodal vertices is the vertex set…

Klee–Nevo–Novik–Zheng conjecture. Then

Klee–Nevo–Novik–Zheng's conjecture. There exists a unique polytopal complex ${\mathcal C}$ in ${\mathbb R}^d$ such that: (i) one face of ${\mathcal C}$ is the cross-polytope…

The polytopal cellulation conjecture. There exists a unique polytopal complex $\mathcal C$ in $\mathbb R^d$ such that: (i) one face of $\mathcal C$ is the cross-polytope…

Let $P$ be a centrally symmetric simplicial $d$-polytope. The higher cs lower bound conjecture. If, for some $3\leq r<\left\lfloor\frac d2\right\rfloor$, … then … Here…

Let $\Delta$ be a centrally symmetric simplicial complex of dimension $d-1\geq 3$. Assume that $\Delta$ is a homology sphere, a connected homology manifold, or a normal pseudomanif…